Abstract : In this thesis, we investigate the DC Programming and DCA approaches in DataMining. More precisely, we are interested in the sparse approximation problems in sparse modelling. The work focuses on theoretical and algorithmic studies, mainly based on DC Programming and DCA. We established interesting properties concerning DC and quadratic reformulations for these problems with the help of new exact penalty techniques in DC programming. These results give new insights on these sparse approximation problems and so allow a better understanding and a better handling of these problems. These novel techniques were applied in both contexts of sparse eigenvalue problem and sparse approximation in linear models.The simple and nice structure of the obtained reformulations are suitably adapted to DC programming and DCA. Computational experiments are very interesting and promising, illustrating the potential of the novel approach.